On stochastic properties of random age and remaining lifetime for populations of manufactured items

The distribution of a random initial age (age composition) of an item is crucial for obtaining its remaining lifetime. A random initial age naturally arises when, for example, an item is drawn at random from a population of continuously manufactured and incepted into operation items. We consider heterogeneous populations of items with lifetime distributions indexed by a frailty parameter. We study different stochastic comparisons for the random age and the remaining (residual) lifetime for items from these populations. The ageing properties for the age composition and remaining lifetime are also discussed. Some examples are provided.